By: Elizabeth Daugherty, Maura Porter, and Molly Kaniger

ALTERNATE INTERIOR ANGLES THEOREM

Definition: When two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.
Alternate Interior Angles: L3 and L6 is an example of Alternate Interior Angles.







Ex. 1: Looking at the figure above, if lines k and l are parallel, locate the alternative interior angles. According to the Alternative Interior Angles theorem, are these angles congruent?

line y and z are parallel, name the alternating interior angles
Answers
Ex. 1- 2&8, 3&5. Yes.

Prove the Alternate Interior Angles theorem

2. Given L1 || L2
Prove 4 is congruent to 6

Answer:
1. L1 || L2 Given
2. 4 is congruent to 8 Corresponding Angles Postulate
3. 8 is congruent to 6 Vertical Angles Congruence Theorem
4. 4 is congruent to 6 Transitive Property of Congruence

ALTERNATE EXTERIOR ANGLES THEOREM

Definition:
When two parallel lines are cut by a transversal, the resulting alternate exterior angles are congruent.
Alternate Exterior Angles: L1 and L8 is an example of Alternate Exterior Angles.


Ex. 1: Looking at the figure above, if lines k and l are parallel, locate the alternate exterior angles. Are these angles congruent? Why or why not?


name alternating exterior angles
Answers
Ex. 1: 1,7 4,6. Yes, due to the Alternate Exterior Angles Theorem.